A topologically charged four-dimensional wormhole and the energy conditions

In this research work, our primary focus revolves around the examination of a specific category of traversable wormholes known as topologically charged generalized Schwarzschild-Simpson-Visser-type wormhole, $ds^2=-\Big(1-\frac{2\,M}{\sqrt{x^2+b^2}}\Big)\,dt^2+\Big(1-\frac{2\,M}{\sqrt{x^2+b^2}}\Big)^{-1}\,\Big(\frac{dx^2}{\alpha^2}\Big)+(x^2+a^2)\,(d\theta^2+\sin^2 \theta\,d\phi^2)$. This wormhole is uniquely defined by a pair of key parameters (length scales $a$ and $b$), together with the global monopole charge $\alpha$. A noteworthy outcome of our investigation is the observation that the energy-momentum tensor associated with this wormhole complies with both the weak energy condition (WEC) and the null energy condition (NEC). Furthermore, incorporation of global monopole charge introduces a substantial influence on the curvature properties of wormhole space-time and various associated physical quantities derived from this geometry.